Natural selection is ineffective without genetic variation in populations. Genetic correlations between the characters of an organism place constraints on its evolution, because the characters cannot change independently. Neither the causes nor the effects of genetic characters are well understood. The cause will be investigated with models of pleiotropic mutations in complex genetic systems with linked loci, using a combination of analytical and numerical techniques. The effects of genetic correlations will be investigated through the development and application of quantitative genetic methods for multivariate analysis of phenotypic evolution. These studies will help to clarify fundamental and long unresolved questions about adaptation and evolution of correlated characters in natural populations and will also have applications in artificial breeding programs.